Couple of thoughts:
spoilers:end of spoilers
First of all, assuming a past Doctor, it could be that the larger secret of this season is that Time Lords don’t have limited regenerations and that every time they hit 12, typically, they’d have their memory of several erased. So this plays off the Season 2B theory and might have the second Doctor going through ten more incarnations only to have his memory wiped and sent back thinking he’s on the third. It’s probably relevant that none of the multi-Doctor memory rules seem to apply here.
Another possibility is that Gallifrey and the Doctor split off at some point. For simplicity’s sake, let’s say that Capaldi became Whitaker but he also became Ruth and that each Doctor in synced to a version of Gallifrey that matches their actions. One earth, multiple Doctors and Gallifreys with separate personal timelines but sharing one earth and one universe. So we’ve got 13A and 13B and maybe they’ll have to put their timelines back together to become 14.
Another convoluted possibility is that the Doctor’s timeline splinters every time he/she regenerates in the TARDIS as kind of a Schrödinger’s cat thing and so you have branching TARDISes and a bunch of spare companions running around that the Doctor never noticed because of how The Doctor is.
Some weird version of this might allow for the long rumored Rose return and even Amy or Rory if it’s a messy situation where every time the Doctor regenerates or the TARDIS goes somewhere it splinters off and there’s twenty some Brigadiers and Sarah Janes and Claras and Alaric’s and Jamies, etc. roaming around a single earth. Maybe the secret of the Timeless Child is that there’s only one TARDIS that’s been “cloned” through a series of grandfather paradoxes or something like that.
There is, always, the long running theory that there’s only one (or two) Time Lords. I can recall that one dating back years. The idea being that either the same Time Lord is assigned a new identity without memories every twelve or however many allotted regenerations. Or otherwise that Rassilon/Omega/The Other creates duplicates of themselves or their offspring with a grandfather paradox. I think finding out there is only one Time Lord would certainly prompt the Master to do what he did, particularly if he finds out all the Doctors come after him in sequence.
The idea of using a grandfather paradox to duplicate something which causes a grandfather paradox continues to exist without any history required and you can just keep replicating the paradox to create more until you create a whole species by sending the same child back in time with a gun to kill his grandfather six billion times. Every time one succeeds, they become an orphan of a dead future and you can just repeat the process to make more.